相关论文: A Time-Series Foundation Model by Universal Delay …
In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…
The staggering amount of streaming time series coming from the real world calls for more efficient and effective online modeling solution. For time series modeling, most existing works make some unrealistic assumptions such as the input…
Transformer-based methods have achieved impressive results in time series forecasting. However, existing Transformers still exhibit limitations in sequence modeling as they tend to overemphasize temporal dependencies. This incurs additional…
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently, neural dynamics modeling method have become a prevalent…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions…
We propose the time-delayed transformer (TD-TF), a simplified transformer architecture for data-driven modeling of unsteady spatio-temporal dynamics. TD-TF bridges linear operator-based methods and deep sequence models by showing that a…
Credit assignment problem of neural networks refers to evaluating the credit of each network component to the final outputs. For an untrained neural network, approaches to tackling it have made great contributions to parameter update and…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
As multimodal data proliferates across diverse real-world applications, leveraging heterogeneous information such as texts and timestamps for accurate time series forecasting (TSF) has become a critical challenge. While diffusion models…
Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens'…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are…